Frodo Baggins first bears the One Ring in The Lord of the Rings after Bilbo gives it away.
Bilbo leaves the Ring behind when he departs from the Shire, and Frodo inherits it along with Bag End. Gandalf later determines that it is the One Ring forged by Sauron, making Frodo’s possession far more dangerous than either Hobbit initially understands.
Frodo accepts the task of taking the Ring away from the Shire. At the Council of Elrond, the planned destination becomes Mount Doom, the only place where the Ring can be destroyed. Frodo carries it through the journey with help from companions including Samwise Gamgee.
Sam briefly carries the Ring after Shelob’s attack, but that does not make him the principal Ring-bearer of the quest. The important succession begins with Bilbo and then passes to Frodo, whose burden drives the central plot of the trilogy.